Bjørn

diff(log(y(t)),t) produces 'diff(y(t),t,1)/y(t). But same result is also produced by diff(log(-y(t)),t). Proposal: Such integrate('diff(y(t),t,1)/y(t),t) should ask whether y(t)is positive or negative and return log(y(t)) for "positive" and log(-y(t))for "negative".

integrate(1/(-y),y) can be rewritten as - integrate(1/y,y). But we can't conclude log(-y) = -log(y). Maxima has an approach to detect negativ values during integration: 1. integrate(1/(-y),y) -> - log(y) 2. integrate(1/(a-y),y) -> - log(a-y) At least in the 2nd case it seems obvious, that this approach is not sufficient. Proposal: If Maxima has to compute integrate(1/(a-y),y), Maxima asks Is "a - y" positive, negative or zero? (or considers constraints by assume()) and creates the correct result...

'integrate(1/(-y),y)' can be rewritten as '- integrate(1/y,y)'. But we can't conclude 'log(-y) = -log(y)' Maxima has an approach to detect negativ values during integration: 1. 'integrate(1/(-y),y) -> - log(y)' 2. 'integrate(1/(a-y),y) -> - log(a-y)' At least in the 2nd case it seems obvious, that this approach is not sufficient. Proposal: If Maxima has to compute 'integrate(1/(a-y),y)', maxima asks "Is "a - y" positive, negative or zero?" or considers constraints by 'assume' and creates the correct...

'integrate(1/(-y),y)' can be rewritten as '- integrate(1/y,y)'. But we can't conclude 'log(-y) = -lo Maxima has an approach to detect negativ values during integration: 1. 'integrate(1/(-y),y) -> - log(y)' 2. 'integrate(1/(a-y),y) -> - log(a-y)' At least in the 2nd case it seems obvious, that this approach is not sufficient. Proposal: If Maxima has to compute 'integrate(1/(a-y),y)', maxima asks "Is "a - y" positive, negative or zero?" or considers constraints by 'assume' and creates the correct ...

ode2('diff(y,t)-a*(1-y^2/c^2),y,t);

subst, ratsubst: replace subexpression with exponents